Differentiability of quadratic BSDEs generated by continuous martingales

In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward--backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the differentiability of a FBSDE with respect to the initial value of its forward component. This enables us to obtain the main result of this article, namely a representation formula for the control component of its solution. The latter is relevant in the context of securitization of random liabilities arising from exogenous risk, which are optimally hedged by investment in a given financial market with respect to exponential preferences. In a purely stochastic formulation, the control process of the backward component of the FBSDE steers the system into the random liability and describes its optimal derivative hedge by investment in the capital market, the dynamics of which is given by the forward component.Comment: Published in at http://dx.doi.org/10.1214/11-AAP769 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Effects of short-range interactions on transport through quantum point contacts: A numerical approach

We study electronic transport through a quantum point contact, where the interaction between the electrons is approximated by a contact potential. Our numerical approach is based on the non-equilibrium Green function technique which is evaluated at Hartree-Fock level. We show that this approach allows us to reproduce relevant features of the so-called "0.7 anomaly" observed in the conductance at low temperatures, including the characteristic features in recent shot noise measurements. This is consistent with a spin-splitting interpretation of the process, and indicates that the "0.7 anomaly" should also be observable in transport experiments with ultracold fermionic atoms.Comment: 12 pages, 10 figure

Low-rank Linear Fluid-structure Interaction Discretizations

Fluid-structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid-structure interaction model for different solids and different fluids. For instance, a shipping company wants to know how the material, a ship's hull is made of, interacts with fluids at different Reynolds and Strouhal numbers before the building process takes place. Also, the behavior of such models for solids with different properties is considered before the prototype phase. A parameter-dependent linear fluid-structure interaction discretization provides approximations for a bundle of different parameters at one step. Such a discretization with respect to different material parameters leads to a big block-diagonal system matrix that is equivalent to a matrix equation as discussed in [KressnerTobler 2011]. The unknown is then a matrix which can be approximated using a low-rank approach that represents the iterate by a tensor. This paper discusses a low-rank GMRES variant and a truncated variant of the Chebyshev iteration. Bounds for the error resulting from the truncation operations are derived. Numerical experiments show that such truncated methods applied to parameter-dependent discretizations provide approximations with relative residual norms smaller than $10^{-8}$ within a twentieth of the time used by individual standard approaches.Comment: 30 pages, 7 figure

Magnetic dipole excitations in nuclei: elementary modes of nucleonic motion

The nucleus is one of the most multi-faceted many-body systems in the universe. It exhibits a multitude of responses depending on the way one 'probes' it. With increasing technical advancements of beams at the various accelerators and of detection systems the nucleus has, over and over again, surprised us by expressing always new ways of 'organized' structures and layers of complexity. Nuclear magnetism is one of those fascinating faces of the atomic nucleus we discuss in the present review. We shall not just limit ourselves to presenting the by now very large data set that has been obtained in the last two decades using various probes, electromagnetic and hadronic alike and that presents ample evidence for a low-lying orbital scissors mode around 3 MeV, albeit fragmented over an energy interval of the order of 1.5 MeV, and higher-lying spin-flip strength in the energy region 5 - 9 MeV in deformed nuclei, nor to the presently discovered evidence for low-lying proton-neutron isovector quadrupole excitations in spherical nuclei. To the contrary, we put the experimental evidence in the perspectives of understanding the atomic nucleus and its various structures of well-organized modes of motion and thus enlarge our discussion to more general fermion and bosonic many-body systems.Comment: 59 pages, 59 figures, accepted for publication in Rev. Mod. Phys

1. Wochenbericht AL506

Wochenbericht, AL 506 (01.04-08.04.2018

1. Wochenbericht POS 517

(03.09-10.09.2016